Physics-Informed Functional Link Constrained Framework with Domain Mapping for Solving Bending Analysis of an Exponentially Loaded Perforated Beam

This article presents a novel and comprehensive approach for analyzing bending behavior of the tapered perforated beam under an exponential load. The governing differential equation includes important factors like filling ratio (α), number of rows of holes (N), tapering parameters (φ and psi), and exponential loading parameter (γ), providing a realistic and flexible representation of perforated beam configuration. Main goal of this work is to see how well the Domain mapped physics-informed Functional link Theory of Functional Connection (DFL-TFC) method analyses bending response of perforated beam with square holes under exponential loading. For comparison purposes, a corresponding PINN-based formulation is developed. Outcomes clearly show that the proposed DFL-TFC framework gives better results, including faster convergence, reduced computational cost, and improved solution accuracy when compared to the PINN approach. These findings highlight effectiveness and potential of DFL-TFC method for solving complex engineering problems governed by differential equations. Within this framework, hidden layer is replaced by a functional expansion block that enriches input representation via orthogonal polynomial basis functions, and the domain of DE mapped to corresponding domain of orthogonal polynomials. A Constrained Expression (CE), constructed through the Theory of Functional Connections (TFC) using boundary conditions, ensures that constraints are exactly satisfied. In CE, free function is represented using a Functional Link Neural Network (FLNN), which learns to solve resulting unconstrained optimization problem. The obtained results are further validated through the Galerkin and PINN solutions.